{"title":"(n,d)环面的最优虫洞路径","authors":"Stefan Bock, F. Heide, C. Scheideler","doi":"10.1109/IPPS.1997.580921","DOIUrl":null,"url":null,"abstract":"The authors consider wormhole routing in a d-dimensional torus of side length n. In particular they present an optimal randomized algorithm for routing worms of length up to O(n/(d log n)/sup 2/), one per node, to random destinations. Previous algorithms only work optimally for two dimensions, or are a factor of log n away from the optimal running time. As a by-product they develop an algorithm for the 2-dimensional torus that guarantees an optimal runtime for worms of length up to O(n/(log n)/sup 2/) with much higher probability than all previous algorithms.","PeriodicalId":145892,"journal":{"name":"Proceedings 11th International Parallel Processing Symposium","volume":"8 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1997-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Optimal wormhole routing in the (n,d)-torus\",\"authors\":\"Stefan Bock, F. Heide, C. Scheideler\",\"doi\":\"10.1109/IPPS.1997.580921\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The authors consider wormhole routing in a d-dimensional torus of side length n. In particular they present an optimal randomized algorithm for routing worms of length up to O(n/(d log n)/sup 2/), one per node, to random destinations. Previous algorithms only work optimally for two dimensions, or are a factor of log n away from the optimal running time. As a by-product they develop an algorithm for the 2-dimensional torus that guarantees an optimal runtime for worms of length up to O(n/(log n)/sup 2/) with much higher probability than all previous algorithms.\",\"PeriodicalId\":145892,\"journal\":{\"name\":\"Proceedings 11th International Parallel Processing Symposium\",\"volume\":\"8 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1997-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings 11th International Parallel Processing Symposium\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/IPPS.1997.580921\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings 11th International Parallel Processing Symposium","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/IPPS.1997.580921","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The authors consider wormhole routing in a d-dimensional torus of side length n. In particular they present an optimal randomized algorithm for routing worms of length up to O(n/(d log n)/sup 2/), one per node, to random destinations. Previous algorithms only work optimally for two dimensions, or are a factor of log n away from the optimal running time. As a by-product they develop an algorithm for the 2-dimensional torus that guarantees an optimal runtime for worms of length up to O(n/(log n)/sup 2/) with much higher probability than all previous algorithms.
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